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The evolution of

f_{t}

is governed by four parameters:

σ_{Δ a}

⁠,

μ_{m}

⁠,

σ_{m}

⁠, and

ρ_{m}

(see equations [6] and [7]). Table 2a summarizes the posterior for these parameters. The posterior median for

σ_{Δ a}

is somewhat lower than a typical estimate for the United States, but this is consistent with using the OECD average for

f_{t}

⁠. The spread of the posterior is roughly what one would find using 16 i.i.d. normal observations, that is, using

q = 16

low-frequency observations with

Δ f_{t}

an i.i.d. process. The posterior for the average growth rate,

μ_{m}

⁠, is centered around 1.9% per year with 67% error bands of roughly

\pm

1% per year. Figure 3b shows the posterior estimates for

m_{t}

⁠, the local level of

Δ f_{t}

⁠. The posterior median shows some variation over the sample, but a constant value of 1.9% (its mean) is within the (pointwise) 67% credible set for all dates.

Table 2.

Posterior Percentiles

a. Posterior percentiles for selected parameters, $f_{t}$ and $c_{t}$ processes
	Percentiles of Posterior
Parameter	0.05	0.17	0.50	0.84	0.95
i. Parameters for $f_{t}$ process (in percentage points)
$σ_{Δ a}$	2.34	2.70	3.33	4.14	4.87
$μ_{m}$	−0.08	0.77	1.85	2.79	3.56
$σ_{m}$	0.42	0.73	1.13	1.52	1.76
$h_{m}$	50	63	96	133	146
ii. Parameters for $c$ process
$μ_{c}$	−0.97	−0.83	−0.63	−0.45	−0.32

a. Posterior percentiles for selected parameters, $f_{t}$ and $c_{t}$ processes
	Percentiles of Posterior
Parameter	0.05	0.17	0.50	0.84	0.95
i. Parameters for $f_{t}$ process (in percentage points)
$σ_{Δ a}$	2.34	2.70	3.33	4.14	4.87
$μ_{m}$	−0.08	0.77	1.85	2.79	3.56
$σ_{m}$	0.42	0.73	1.13	1.52	1.76
$h_{m}$	50	63	96	133	146
ii. Parameters for $c$ process
$μ_{c}$	−0.97	−0.83	−0.63	−0.45	−0.32

$Δ f_{t} = m_{t} + Δ a_{t}$ ⁠, where $Δ a_{t}$ is $I$ (0) and $m_{t}$ is a low-frequency AR(1) with mean $μ_{m}$ and low-frequency AR coefficient $ρ_{m}$ ⁠. The half-life, $h_{m}$ ⁠, solves $ρ_{m}^{h_{m}} = 1 / 2$ ⁠.

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b. Posterior percentiles for selected parameters, $c_{i, t}$ process
	Half-life			$σ_{c}$			$σ_{(c_{t + 50} - c_{t})}$
	Percentiles of Posterior
	0.17	0.50	0.84	0.17	0.50	0.84	0.17	0.50	0.84
i. Pooled across countries
All countries	130	233	389	0.85	1.10	1.37	0.45	0.63	0.86
OECD	201	338	486	0.74	0.91	1.15	0.35	0.44	0.58
Non-OECD	121	211	342	0.91	1.15	1.40	0.52	0.68	0.89
ii. Selected countries
China	150	222	330	1.00	1.20	1.40	0.59	0.68	0.79
Singapore	111	185	291	0.92	1.13	1.34	0.61	0.72	0.86
Madagascar	148	214	317	1.08	1.24	1.42	0.61	0.72	0.85
Belgium	286	394	507	0.69	0.82	0.98	0.32	0.37	0.44
Russia	78	138	239	0.90	1.10	1.34	0.66	0.79	0.94
United States	303	413	529	0.75	0.89	1.06	0.34	0.39	0.45
Australia	340	461	567	0.71	0.84	1.00	0.30	0.34	0.40
Liberia	50	70	108	1.36	1.51	1.62	1.17	1.34	1.50

b. Posterior percentiles for selected parameters, $c_{i, t}$ process
	Half-life			$σ_{c}$			$σ_{(c_{t + 50} - c_{t})}$
	Percentiles of Posterior
	0.17	0.50	0.84	0.17	0.50	0.84	0.17	0.50	0.84
i. Pooled across countries
All countries	130	233	389	0.85	1.10	1.37	0.45	0.63	0.86
OECD	201	338	486	0.74	0.91	1.15	0.35	0.44	0.58
Non-OECD	121	211	342	0.91	1.15	1.40	0.52	0.68	0.89
ii. Selected countries
China	150	222	330	1.00	1.20	1.40	0.59	0.68	0.79
Singapore	111	185	291	0.92	1.13	1.34	0.61	0.72	0.86
Madagascar	148	214	317	1.08	1.24	1.42	0.61	0.72	0.85
Belgium	286	394	507	0.69	0.82	0.98	0.32	0.37	0.44
Russia	78	138	239	0.90	1.10	1.34	0.66	0.79	0.94
United States	303	413	529	0.75	0.89	1.06	0.34	0.39	0.45
Australia	340	461	567	0.71	0.84	1.00	0.30	0.34	0.40
Liberia	50	70	108	1.36	1.51	1.62	1.17	1.34	1.50

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